(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two parts to the problem: 1.) Is the following a good argument from special relativity for the equivilence of energy and mass?

2.) If 1.) is true, why couldn't a similar argument have been made with pre-Einstein physics?

2. Relevant equations

Just two:

E = mc^{2}/(1 - (v/c)^{2})^{1/2}

E = (1/2)mv^{2}

3. The attempt at a solution

Okay, starting with Einstein's energy equation, then assuming some energy is added to the moving particle. It seems pretty obvious that energy is convertible into mass (because of the speed of light squared factor maybe? see below). But I have some questions. First, of course, does the following show that energy is interchangeable with mass:

E = mc^{2}/(1 - (v/c)^{2})^{1/2}

Particle absorbs some energy E_{0}:

E2 = (mc^{2}+ E_{0})/(1 - (v/c)^{2})^{1/2}

Factor out c^2, which gives:

E2 = (m + E_{0}/c^{2})c^{2}/(1 - (v/c)^{2})^{1/2}

But an energy divided by a velocity squared leaves units of mass (kilogram meters^2/seconds^2, divided by meters^2/seconds^2 ).

Looking at the equation then, we could say that m + E_{0}/c^2 equals a new mass, M, so that

m + E_{0}/c^{2}= M Which can be written in terms of Einstein's energy equation:

E2 = Mc^{2}/(1 - (v/c)^{2})^{1/2}

Which seems to indicate that adding energy E_{0}to E yields an increase in mass.

Is that fairly decent so far? If so, here's my problem:

If the above is right, why can't we make the same argument for Newtonian physics?(or maybe, why didn't they?)

Starting with the kinetic energy equation:

E = (1/2)mv^{2}

add E_{0}

E2 = (1/2)mv^{2}+ E_{0}

factor out (1/2)v^{2}, which gives:

E2 = (m + E_{0}/v^{2}) *(1/2)v^{2}

where E_{0}/v^{2}is again in units of mass, because an energy divided by a squared velocity leaves units of mass. This seems to me to indicate that even in pre-Einstein physics energy is interchangeable with mass. Clearly this is incorrect (and yes, it is purely academic, since obviously Newton's energy equations are less accurate than Einstein's).

So, can someone please explain to me what is wrong with all this? Was I correct in the first part (relativity part)?

Thanks, as always!

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# Homework Help: Special Relativity: Energy and Mass

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